Distance Modulus Calculator

The distance modulus is the difference between an object's apparent magnitude and its absolute magnitude. A simple logarithmic formula converts this difference into an actual distance in parsecs.

Because the absolute magnitude can be estimated for standard candles like Cepheid variables, the distance modulus lets astronomers measure distances to objects far beyond the reach of direct parallax, forming a key rung of the cosmic distance ladder.

Use d = 10 pc times 10 raised to the power of the distance modulus divided by 5. A distance modulus of 0 corresponds to 10 parsecs, 5 corresponds to 100 parsecs, and 15 corresponds to 10,000 parsecs. Multiply parsecs by 3.26 to get light-years.

This calculator uses the plain distance modulus, m − M = 5 log(d/10). Interstellar dust dims a star by an extinction A magnitudes, so the observed modulus overstates the distance. The true (extinction-corrected) distance modulus subtracts it: (m − M)₀ = m − M − A = 5 log(d/10). If your simple result comes out too far, unmodeled reddening A is usually the reason; subtract the extinction in magnitudes before converting to distance.